A Research on the Generalizations of Modules Whose Submodules are Isomorphic to a Direct Summand

Year 2024, Volume: 17 Issue: 1, 268 - 278, 28.03.2024

Fatih Karabacak , Özgür Taşdemir

https://doi.org/10.18185/erzifbed.1371910

Abstract

A module M is called virtually semisimple (resp. virtually extending) if every submodule (resp. complement submodule) of M is isomorphic to a direct summand of M. It is known that virtually extending modules is a generalization of virtually semisimple modules. In this paper, the relationships between virtually extending modules and other generalizations of virtually semisimple modules are examined. Moreover, we introduce a new generalization of virtually semisimple modules; namely CH modules: We say a module M is a c-epi-retractable (or briefly CH module) if any complement submodule of M is a homomorphic image of M. CH modules contains the class of virtually extending modules and the class of epi-retractable modules. We also give some basic properties of this new module class.

Keywords

virtually extending module, epi-retractable module, CH module, virtually semisimple module

Ethical Statement

There are no ethical issues regarding the publication of this study.

Supporting Institution

Anadolu University Scientific Research Projects Commission

Project Number

2210E164

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